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If the expansion of (x + y)^n has 15 terms, what is the value of n?

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Question: If the expansion of (x + y)^n has 15 terms, what is the value of n?

Options:

  1. 14
  2. 15
  3. 16
  4. 17

Correct Answer: 14

Solution: 

The number of terms in the expansion of (x + y)^n is n + 1. Therefore, n + 1 = 15, which gives n = 14.

If the expansion of (x + y)^n has 15 terms, what is the value of n?

Practice Questions

Q1
If the expansion of (x + y)^n has 15 terms, what is the value of n?
  1. 14
  2. 15
  3. 16
  4. 17

Questions & Step-by-Step Solutions

If the expansion of (x + y)^n has 15 terms, what is the value of n?
  • Step 1: Understand that the expression (x + y)^n is a binomial expression.
  • Step 2: Know that the number of terms in the expansion of (x + y)^n is given by the formula n + 1.
  • Step 3: Set up the equation based on the information given: n + 1 = 15.
  • Step 4: Solve for n by subtracting 1 from both sides of the equation: n = 15 - 1.
  • Step 5: Calculate the value: n = 14.
  • Binomial Expansion – The expansion of (x + y)^n results in n + 1 terms, where n is a non-negative integer.
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